He’s referring to the hunt for Osama bin Laden and the difficulty of pursuing leads based on potentially valuable intelligence from potentially unreliable sources – but his tautological observation could just as easily apply to the film’s complex, matter-of-fact, procedural approach to a ten-year operation filled with multiple false leads, contentious techniques, moral crises and, ultimately, a ruthlessly efficient military strike.

Eschewing the kind of easy through-line that might conceivably have shown by cause and effect how American forces finally captured and killed bin Laden, Bigelow and screenwriter Mark Boal (who wrote Bigelow’s The Hurt Locker) instead dramatise how fraught with difficulty and uncertainty each line of inquiry was as administrations changed and the means for achieving their objectives altered.

Based on first-hand accounts, but necessarily fictionalised, Zero Dark Thirty does not – as some have claimed – definitively conclude that torture facilitated bin Laden’s capture. Rather, the scenes depicting so-called “enhanced interrogation” provide important context. Because these techniques were used, the film seems to be saying, we don’t know how this story might have turned out had they not been part of the Bush administration’s immediate post-9/11 anti-terrorism strategy. Thus not to show them would have risked whitewashing the tale and turning it into a jingoistic slice of American triumphalism.

Nevertheless, part of the reason these scenes have such an impact is the forthright way Bigelow introduces them. Zero Dark Thirty begins with a blank screen and the harrowing sound of anguished, real-life, emergency phone calls from the World Trade Center on 11 September, 2001. For close to two minutes that’s all we get and the effect is devastating.

Those making and receiving the calls are the first distressed inhabitants of a new world and when Bigelow cuts to her first scene, the revenge-tinged ugliness of the American response to this new world becomes plain to see. Suddenly we’re in a CIA “black site” two years later with a bearded American agent by the name of Dan (Jason Clarke) attempting to extract information from a Muslim prisoner strung up by his arms from the roof of a jail cell. What follows is brutal. Beaten, waterboarded and humiliated, the prisoner is thoroughly dehumanised by his American captors and Bigelow’s camera, framing the action simply and without judgment, doesn’t flinch.

These scenes also introduce us to Maya (Jessica Chastain), a young, newly appointed field agent so fresh from Washington that she’s turned up in a suit. Blanching at her first encounter with waterboarding, she quickly adjusts, rejecting Dan’s offer to observe the interrogation from a monitor and following his lead by not covering her face when she re-enters the cell with him. It’s a smart way of quickly establishing her resolve and adaptability and the rest of the film follows her search for bin Laden as she gradually shuts herself off from everything beyond her desire to kill her target.

Furnished with only minimal details about her background, she’s a fascinating character and Chastain is astonishing in the role, not because it’s a particularly showy part (although she is in almost every scene), but because she remains such an enigma. Here, the chameleon-like quality that has made Chastain simultaneously the most in-demand and the most inconspicuous actress of the last two years works to her advantage. Her character is defined by ruthlessly executed action and, as such, the film becomes an almost fetishistic tribute to her and her colleagues’ relentless professionalism.

The persistent, low-level tension is, of course, jacked up several notches during the climactic assault on bin Laden’s compound in Abbottabad, Pakistan. As with the combat scenes in The Hurt Locker, Bigelow doesn’t use gung-ho theatrics to achieve this. Shot mostly in night vision, it’s depicted matter-of-factly without swelling music or Hollywood heroics, with an ambiguous final shot that hints at the unknowable cost of revenge. Zero Dark Thirty is a stunning achievement: a deftly made, intelligently handled and serious piece of film-making that stands alongside Paul Greengrass’s United 93 as the definitive cinematic responses to 9/11.